The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 X X 1
0 X 0 0 0 0 X 2X 2X 0 0 X X X X X X 0 X 0 2X X 2X X 0 X 0
0 0 X 0 0 X 2X 0 2X 0 X X 2X 2X 0 X 0 X 0 X X 2X 2X X X 2X 0
0 0 0 X 0 2X 2X X 0 X X 0 0 X 2X X X 0 X 2X 0 X X X X 2X 0
0 0 0 0 X 2X 2X 2X 2X 2X 0 2X 0 0 2X 2X 0 2X X 0 0 2X 2X 0 X 2X X
generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 48.
Homogenous weight enumerator: w(x)=1x^0+80x^48+192x^51+238x^54+166x^57+12x^60+2x^63+22x^66+12x^69+2x^72+2x^75
The gray image is a linear code over GF(3) with n=81, k=6 and d=48.
This code was found by Heurico 1.16 in 0.866 seconds.